Simple as it is, I made a couple errors trying to traverse the diagram, beginning with the very first choice.

My globe has Istanbul, but I went off on the left path, not noticing that the order of the labels was reversed from the order in the question. It didn’t take long too realize the error, but I almost didn’t catch my second error.

I was trying to follow the “no” branch from the Bangladesh node, and I mistakenly ended up at the United Arab Republic node. Apparently following a line is harder than I thought.

Once I had my errors fixed, the diagram dated my globe to the range 1961 to 1964. In the course of doing a little more exploring, I discovered the manufacturer of the globe, Replogle Globes, has a How Old is Your Globe? page. It’s a list of 100+ countries that have changed names since 1939.It’s not as fun as the XKCD chart, but it’s more complete, especially in the period of my globe, though I still had to supplement it with Wikipedia to get the exact dates of the name changes.

Interestingly, the results are both precise and slightly conflicting. My globe has Zambia, which was Northern Rhodesia until October 24, 1964, and it has the United Republic of Tanganyika and Zanzibar which only existed for six months ending on October 29, 1964. That gives an amazingly precise origin window of only five days. However, the globe also denotes Malta as being a British territory even though Malta gained independence on September 21, 1964. I’m guessing the globe is from late 1964 or early 1965 with the Malta indication (and possibly Tanzania) being out of date. Regardless, 50 years is about right for the age.

The globe is in pretty good condition and has a two axes of rotation, making it easy to get a good look at Antartica, for instance.